Holomorphic and analytic functions, power series, Cauchy integral and Cauchy integral formula, meromorphic functions and differential forms, calculus of residues and applications, analytic continuation, conformal mappings, Riemann mapping theorem, Laurent series and conformal classification of annuli, harmonic functions and Dirichlet problem, introduction to Riemann surfaces, theory of elliptic functions and integrals. (Math MATH 106 offers a less theoretical treatment). Prerequisites: Math MATH 51, MATH 52 and MATH 171, or 61CM and 62CM.
4 units · Letter or Credit/No Credit · GER: WAY-FR
Holomorphic and analytic functions, power series, Cauchy integral and Cauchy integral formula, meromorphic functions and differential forms, calculus of residues and applications, analytic continuation, conformal mappings, Riemann mapping theorem, Laurent series and conformal classification of annuli, harmonic functions and Dirichlet problem, introduction to Riemann surfaces, theory of elliptic functions and integrals. (Math 106 offers a less theoretical treatment). Prerequisites: Math 51, 52 and 171, or 61CM and 62CM.
Offered in Autumn 2025 at Stanford University.